which is referred to as the occupied set. We say that
percolation occurs if \({\mathcal {C}}(\Pi ^\lambda )\)  contains a connected
unbounded component. Following Section 2.1 in [1]},
one can use ergodicity to prove that percolation is a 0-1 event.
It is therefore natural to define the critical threshold
\(\lambda _{c,\Theta }=\lambda _{c,\Theta }(L)\)  for which percolation
occurs by letting
\( \lambda _{c,\Theta }:=\inf \lbrace \lambda >0: {\mathbb {P}}({\mathcal {C}}(\Pi ^\lambda ) \textrm { percolates})=1\rbrace .\) 
